alford



' April 1948- A. ALFORD 3 22,993

MATCHING NETWORK Original Filed Nov. 19, 1936 3 Sheets-Sheet} FIG.2.

FIG.1.

INVENTOR ANDREW ALFORD ATTORNEY April 20, 194 8. ALF oRD Re; 22,993

MATCHING NETWORK Original Filed Nov. 19, 1936 I5 SheetsSheet;2

FIG].

- INVENTO-R ANDREW ALFORD ATTORNEY I April 20, 1948. A. ALFORD 22,993

MATCHING NETWORK Original Filed Nov. 19, 1936 3 Sheets-Sheet 3 K FIG".

0 J I Y L w o v 7- .5 1.0 1.5 I 2.0 [NVENTOR AND/PE W ALI-OED ATTO R NEY Reissuecl Apr. 20, 1948 MAroiiiNG NETWORK Andrew Alford, Cambridge, Mas s assignor to Mac" my Radio and Telegraph; Coinjranfi New York, N.Y.,acorporation "ofliehwafe Original No. 2,165,086, dated No. 111,643,Novcn bcr'19, 193G.

cember 21, 1938. Application f reissueiviafen 19, 1945, Serial No.583,401

13 Claims.

This invention relates to matching'network's and pertains moreparticularly to networks of this character for interconnecting radioapparatus with two-wire transmission lines;-

It is an object of this invention to provide an electrical network forinterconnecting a radio transmitter with a two-wire transmission line sothat it will always be insured that the two 0011'- ductors of thetransmission linecarry equal cur rents 180 out of phase.

Another object is the provision of an electrical network forinterconnecting a radio translating device with a two-wire circuitwhereby equal voltages between the two wires of the circuit and theground will be obtained and at-th'e same time a 180" phase relationbetween the currents the two wires will result.

Whenever two-wire transmission lines are used tosupply power to thetransmitting antennae; it is necessary to'insure' that the two"conductors of the transmission-line carry equal-currents 180 out ofphase so that the" transmission line-itself will not-act as an antennaand r'adiate' 'energy in all directions; When the currents inth'e"trans-' mission line are characterized as above men= tinned, theline acts'merely as a conductor to transfer the energy to the antenna;and undesira ble radiation from the transmissionline itself is avoided:v

Transmission-lines can very wellbe balanced at the lower radio frequencyranges by the use of'know'n apparatus and methods with sat-isfac tor'y'results, but as the frequency is increased difficulties are encounteredwhichhave" not been overcome by the'teachings of the prior art; Forexample, with frequenciesof the order of nve megacycles the problein' ofsupplying the line with energy'in a balanced manner-may be" sans:factorily solved by a number ametnoasemploj: in'g air core transformers.

At frequencies of the or 2: stashed at this 'Irequen'cy electrostaticessentials nior''eflic'iiit and exerts agreater distiiittiiiieifct.--Avail higher frequencies the difliculties encounteredare evengreater.

daryof the transg sure that the center of t s 661i shall be-at'Z'eropotential. This con-'- dition is difficult to achieve however,since the ginseng c "o'nnection*- must necessarily have somefihys'iai'liig th and consequently some induster-ice; 'this ind fiancebeir'ig' usually high enougn s'o' thatthe droiia'cross the groundingwire at the higher frequencies is sufficient to produceafid'niigeotefiaar a't' 'the' eer'iter of; the coil instead are 6'dfidteiitial -with the result that capacity coupliiigbtweii the primaryand secondary of the transformer results and produces the usualundesirable efiect.

A large number of other arrangements have been suggested for obtain-iiiga balanced condition in transmission lines, but so far as I am aware thevarious known arrangements are either ex-' tremely complicated andexpensive to construct or fail to give a balanced output at the higherfrequency ranges.

I have found that it is possible to avoid the difiicultiesdue-tocafiadity-coupling by the pro-- vision of an electrical networkwhich is relatively simple-and 'hasbeen found'to give very satisfactoryresults in actual practice.

In accordance with--niyinvention I provide a network of impedanc-esconnected across and in series with the line and between line and groundwhich serve weanlin -the use, causing it to 3 iment of my inventionwherein two inductances and a condenser are used.

Figs. 2 and 3 illustrate other networks in accordance with my invention,utilizing two condensers and an inductance.

Fig. 4 illustrates another network in accordance with my inventionutilizing two inductances and a condenser.

Figs. 5 and 6 are diagrams used in explaining the operation of thenetworks shown in Figs. 1 and 2, and in Figs. 3 and 4, respectively.

Figs. '7, 8, 9 and 10 shOW various circuit arrangements utilizing thenetworks of Figs. 1, 2, 3 and 4.

Figs. 11 and 12 are used in further explanation of the invention.

Referring more particularly to the drawings,

in Fig. 5 the voltage between the wires I4, and

2'l, is V and the voltage between wire 21 and the point 3 is U, the wire2! being connected to ground in such manner that it is really at groundpotential or if not, so that it may be assumed to be at ground or otherfixed potential. The impedance impedance 3-5 is C and the impedance 3-4,representing the transmission line impedance is P. Likewise the currentthrough the impedance A is M, and the current through. the impedance Pis N.

The power for supplying the currents mentioned, which may for example bederived from a vacuum tube, is assumed to be applied between terminals land 2 while the transmision line, represented by impedance P, isconnected to terminals 3 and 4.

Now the condition desired to be attained is that the voltage U betweenthe point 3 and ground, and the voltage V between the point 4 andground, shall be equal in magnitude and opposite in phase, that is V=-U.e

This result is secured when the relative'values and signs of theimpedances are properly chosen as shown by the following formulae,

expanding and rearranging terms .(6) becomes then Equation 10 becomes 85is A, the'impedance 5-6 is B, the.

which may be expanded as (12) jbr+jar%jarbcac bsasab+-%as=0 Equatingimaginary and real components separately we derive two separateEquations 13 and ,Now substituting (--a) for (b-l-a) in Equation 13 Weobtain c=-2b or 0:: 2B

Thus the condition that V=U regardless of the value of P may besatisfied by the two circuits shown in Figs. 1 and 2 provided thatelements of the same kind, that is the two inductances in Fig. 1 and thetwo capacitances in Fig. 2 are equal, and when the third element is suchthat the impedance across it is equal in magnitudeto one-half of theimpedance of either one of the equal elements, and has an opposite sign.To assure this result the two inductances in Fig. 1 must be arranged insuch manner as to avoid or at least keep very small, mutual reactancebetween them. And the third element must be arranged in such manner thatthe impedance from the junction point of the inductances in Fig. 1 toground is equal in magnitude to one-half of the impedance of either oneof the inductances, and is of-opposite sign. But this impedance need notbe necessarily concentrated in the third element itself, that is, it isnot necessary that the condenser represented in Fig. 1 should have theexact value of impedance for, for instance, it is entirely possible forpart of this impedance to be concentrated in the lead which is necessaryto connect this condenser to ground so that in actual practice it maywell be that the reactance of the condenser is actually much higher thanthat which is required; yet a part of it is balanced out by thereactance of the lead which connects the condenser to ground or for thatmatter partially by the inductance of the lead which connects the otherside of the condenser to the junction point of the inductances.

The same, of course, is true of Fig. 2, namely this time the inductanceshown as the third element is not necessarily concentrated in the coilitself but partially at least isto be found in the wire which connectsthis inductance to ground or to the junction point of the twocondensers. It is this ieature of the circuit which makes it reallypractical for with this circuit it is not necessary to find a point inthe transmitter that is really at ground potential. Indeed all that isnecessary is that the impedance between the junction point of (1:0 orA=C the" similarelements and ground-have the required value.- "It hasbeen found experimentally that'the distributed capacit'y of theinductors to ground utilized in circuit I does not in practice disturbthe circuit to anygreat extent. The same is true of the stray capacitiesto ground of the condensers utilized in circuit 2. This is quitereasonable from the theoretical point of view for the over all effect ofsuch stray" capacities to ground is merely to alter'the impedancebetween points 3 and 4 respectively to ground, that is, in effect merelyto alter the-impedance of the transmission line as seen from terminals'3 and 4. We have already shown above that as long as the fundamentalconditions of the circuit are satisfied it is quite immaterial as towhat the impedance of the line happens to befor the conditions-to besatisfied by-the three elements are the same irrespective of the valueofthis impedance.

The circuits 3 and 4 may best be explained in connection with Fig. 6.This figure differs from Fig. 5 only in that an impedance has beenplaced between points 4 and 8 rather. than between points-3 and 5. Theanalysis of this circuit is very similar to the one which has alreadybeen carried out in connection with Fig. 5.

Assuming that V represents the voltage between conductors l--8 and 2-4;U the voltage between point 3 and ground, that'is conductor 2-! and X isthe voltage between the point 4 and conductor 2-4, then for a conditionor perfect balance we have I]: X.

This result is secured when the relative values and signs of theimpedances are properly chosen as shown by the following formulae.

20 v V: DM+ E(M+ N) 22- U: (M+ ME adding Equations 22 and 23, we get(24) X+U=NP+2(M+N)E substituting 19 in 24, we get (25) NP=-2ME-2NE orcollecting terms (26) N(P+2E) =2ME substituting 21 in 26, we get (27)(P+2E)D=-2E(F+P) expanding, we get Now assuming that D, E and F are purereactances equal to id, :ie and 9' respectively, and that P is equal tor+:is, then Equating imaginary and real components separately we derivetwo separate equations 30 and 31, as follows:

New substituting -d for 2c in Equation 30, we obtain Consequently'thereaet anc'esF and" D must be equal in magnitude "and apposite insignal-id reactance E must have one-half "the value of reactanc'e D'andmustequal'insign'rea'ctance F. The two possibilities are" illustrated in"Figs. 3 and 4.

In actual practice it has been found convenient to connect circuits ofthe type illustrated in Figs. 1, 2, 3 and 4. to the tank circuit. of thelast amplifier stage in the transmitter ina manner shown in Figs. 7, 8,9 and 10. The-method shown in Fig. '7 when employed in connection withthe circuit shown in Fig. 1 possesses the advantage that both conductorsat the transmission line are connected directly to ground during theoperation of the circuit so that any static charges which may accumulateon the antenna during rain or snow can leak off to ground whereby highstatic potentials may be avoided without the use of any auxiliaryresistors or other means of grounding the transmission line. Moreover,the adjustments obtainable from this type of circuit are sufiicient-totake care of a fairly wide range of line impedances so that even whenthe transmission line isnot flat, that is when it is not perfectlymatched to the antenna, the tank circuit of the transmitter may still beproperly loaded and the'powcr transferred from the 'last amplifier tothe transmission line in an eiiicient way. It has also been found inpractice that the circuit shown in Fig. 8 is particuarly well adaptedfor use in conjunction with the circuit shown in Fig. 2 for in thiscasethe' impedance which is usually obtained between terminals I and 2is capacitative so that part'of the inductance IE! is already balancedoutand condenser Il may be fairly large and consequently the adjustmentsare notyery critical and it is found that the tank circuit .maybe'loadcd'with reasonable case without the use of unreasonablecapacities and inductanccs.

Either one of the circuits shown in Figs. 3 and 4 may be employedinconnection with the arrangements shown in Figs. 7 and 8. The circuitshown in Fig. 9 may also'be used in conjunction with any one of the fourcircuits shown in Figs. 1, 2, 3 and 4 when the impedance of the line issuch that this circuit is more advantageous. Fig. 9 illustrates theconnection when the circuit of Fig. 4 is employed, and Fig.110illustrates the connection whenthe circuit'of Fig. 3 is used. Thenetwork components used for obtaining balance are in the circuitsof'Figs. 7, 8, 9 and 10 isolated from the high direct current potentialsused on the plate of the last tube, by a transformer, usually of thestep-down type, and therefore these components andespecially thecondensers may be relatively cheap in construction. The use oftransformer coupling with grounded secondary reduces the danger of highdirect current plate potentials reaching the line.

In order that the losses in the coils employed in any one of the fourcircuits described above may be kept low it is of course necessary tochoose the proper values of inductances and capacitances.

An explanation will now be made as to how the values of inductance andcapacitance can be determined for most eflicient operation. Thisexplanation will be made in connection with Figs. 1 and 2 since themethod employed in connecare R where L is the inductance of the coil and(:21 times the frequency.

7 The value of Q for ordinary transmitting coils is fairly well knownand is usually somewhere around 150 or 200.

Upon the assumption that the Q factor and hence the resistance of thetwo coils of equal inductance, shown in Fig. l, is the same the totalloss H in both Coils may be expressed by the formula On the other hand Wthe power delivered to the line is Now if we assume that, as is usuallythe case, the impedance P of the transmission line is a pure resistance(1. e. if we assume that is=0 and r=P) and if we remember that A=C (asshown by Equation 1'7) then We may write Equation 5 as follows:

37 M: N(i+ 1) But since impedance A=R+fiwL and since this impedance isvery nearly a pure reactance we may replace A by awL in Equation 37 thusgiving T 38 M: NQT r 1) Substituting this in 35, we obtain Hence theloss H is the two coils depends upon the useful power W which in anygiven case is fixed, the factorQ of the coils which is made as large aspossible, and the coefficient K which depends upon I as may be seen fromthe Equation 41.

Fig. 11 shows how the loss H in the two coils varies with the dimensionsof the two coils, or rather, with the value of From this figure is'maybe seenthat the smallest value of K, that is the least losses for agiven power output and a given Q factor, are obtained when Is equal to.707. The value of K corresponding to such a value of From Fig. 11 itmay be seen that the minimum is not at all sharp but there is a wholeregion where the losses are reasonably low. In actual practice, it isgenerally possible to design the circuit in such a manner that thecircuit operates somewhere within this minimum loss region. It is quiteobvious from Fig. 11 that small coils and large condensers are to beavoided in spite of the usual rule which is very often followed, namely,that for minimum loss small coils and large condensers are to bepreferred. Fig. 11 definitely shows that this rule does not apply to thecircuit shown in Fig. 1.

A similar calculation in connection with the circuit illustrated in Fig.2 gives the following Then Equation 42 may be written as (42A) H K Thisresult is illustrated in Fig. 12. From this figure again it may be seenthat there is a certain best value of condensers and inductances to beused in this second circuit for minimum loss but again the region isfairly wide and in practice it is fairly easy to choose values ofcondensers and reactances which fall within the minimum loss region.

The smallest value of K1 corresponding to the least losses for a givenpower output W and a given coil factor Q occurs when The value of K1 forthis condition is 2.00. It will be noted that this minimum value of K1is about 29 percent lower than the minimum value of K for the circuit ofFig. 1. g

It may be pointed out that a circuit employing two condensers andreactor is somewhat more efiicient. from the point of view of loss thancircuit l which employed two reactors and only one condenser. However,circuit I possessed other advantages. In practice, of course, the lossesin circuit l are quite low so that very often other advantages, ofcircuit I may out-weigh the low loss property of circuit 2. On the otherhand, when the losses are the controlling feature and grounding isprovided for in some other manner, circuit 2 may be preferred. The samesort of considerations apply to circuits illustrated in Figs. 3 and 4.

From the preceding description it will be seen eases that 1 on theassumptiomthat the impedancesare pure-reactances the balance or the-linewill not be aflfected by a change in the load. Furthermore even when theresistive components of the inductance coils-used are taken into accountfrom the stand-point'of-losses it willbe-noted thatthe power loss isnotgreatly "aflected by moderate changesin-theload.

1 While 'I have described certain embodiments of my: invention for the--pur-poses-'-' or illustration, it will be understood thatvarious-modifications and adaptations thereof may be made withi'mt'hespirit oft-he invention as set forth in the appended claims.

What I claim is:

1. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line are of substantiallyequal magnitude and opposite phase comprising three reactances, two ofwhich are of the same sign and the third of which is of the oppositesign, one of said three reactances being connected in series in one ofsaid two wires, another in shunt to said two wires, and the thirdbetween one of said two wires and ground.

2. A system in accordance with claim 1 (wherein the two reactances ofthe same sign are of equal value and the impedance of the thirdreactance is equal in magnitude to one-half that of either of said tworeactances first mentioned.

3. An electrical network having two input terminals and two outputterminals and adapted to maintain voltages equal in magnitude andopposite in sign, between each of said output terminals and a. given oneof. said input terminals, comprising three reactanoes two of which areof the same sign and the third of which is of the pposite sign, thefirst of said three reactances being connected in series between aninput terminal and an output temiinal, a second of said reactances beingconnected between the same said input terminal and the other of saidoutput terminals and the third of said reactances being connectedbetween said other output terminal and the other of said inputterminals.

4. An electrical network according to claim 3 wherein said first andsaid second of said reactances are of equal magnitude and opposite signand said third reactance is of'the opposite sign as said secondreactance and of one half its value.

5. An electrical adapted to maintain equal voltages between each of twooutput temrinals and a given one of two input terminals comprising threereactances, a first and a second of the same sign and a third of theopposite sign, each having a first and a second terminal, all of saidfirst terminals beingconnected together, the second terminals of saidfirst and third reactances constituting said two input terminals and thesecond terminals of said first and second reactances constitutlngsaidtwo output terminals.

6. An electrical network in accordance with claim 5 wherein said firstand second reactances are of the same sign and of equal magnitude andsaid third reactance is such that the impedance across it is equal inmagnitude to one-half of the impedance of either said first or saidsecond impedance and has an opposite sign.

7. In a radio system, radio translating apparatus including anamplifying tube, a two wire transmission line and means forinter-connecting said apparatus and said line so as to minimize energytransfer between said line and the surrounding space, comprising anetwork or three reactances, "two-of which are of the same sign andthe'third ot-"which is of the; Opposite sign,

to the output circuit of said amplifying tube, and

means connecting said tuned circuit-across two of the reactances ofsaidnetwork. 8. In a radio system; radio translating apparatu'sincludingan" amplifying tube, atwo wire transmission lineconnected thereto, meansi for interconnecting said; apparatus and said 'lineso as-tomini-mizeenergy transfer "between said-line and the surrounding, space,comprising a network of three reactances, two of which are of the samesign and the third of which is of the opposite sign, one of said threereactances being connected inseries inone of said two wires, another inshunt to said two wires, and the third between one of said two wires andground, a first tuned circuit connected in the plate circuit of saidamplifying tube, a second tuned circuit magnetically coupled to saidfirst tuned circuit, means connecting said second tuned circuit acrosstwo of the reactances of said network, and means connecting to ground a,point in said second tuned circuit.

9. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line are of substantiallyequal magnitude and opposite phase comprising three reactances, areactance of one sign being connected in series in one of said twoWires, a reactance of the same sign being connected in shunt to said twowires and a reactance of the opposite sign being connected between saidtwo wires and ground.

10. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line are of substantiallyequal magnitude and opposite phase comprising three reactances, two ofwhich are of the same sign and the third of which is of the oppositesign, a reactance of one sign being connected in series in one of saidtwo wires, a reactance of the opposite sign being connected in shunt tosaid two wires and a third reactance having the same sign as saidreactance of one sign connected between one of said two wires andground.

11. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line interconnecting a sourceand a load are of substantially equal magnitude and opposite phasecomprising three reactances, two of which are inductive and equal inmagnitude and the third of which is capacitative and has a magnitudeequal to one-half that of either of said inductive reactances, one ofthe inductive reactances being connected in series in one of said twowires, the capacitative reactance being connected in shunt to said twowires and the other inductive reactance being connected between one ofsaid two wires and ground, the impedance in ohms of each of saidinductive reactances being equal to .707 times the resistance of saidline together with said load.

12. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line interconnecting a sourceand a load are of substantially equal magnitude and opposite phasecomprising three reactances, two of which are capacitative and equal inmagnitude and the third of which is inductive and has a magnitude equalto one-half that of and opposite in sign between each terminal of saidfirst pair and a given terminal of said second pair, comprising threereactances two of which are of the same sign and the third of which isof the opposite sign, the first of said'three reactances being connectedin series between a terminal of said first pair and a terminal of saidsecond pair, a second of said reactances being connected between thesame said terminal of said first pair and the other of said terminals ofsaid second pair, and the third of said reactances being connectedbetween said other terminal of said second pair and the other terminalof said first pair. I

ANDREW ALFORD.

